Pith Number

pith:D5YWL5D7

pith:2017:D5YWL5D7AZBC7NOARRVR4GEB3P

not attested not anchored not stored refs pending

Periods, cycles, and $L$-functions: a relative trace formula approach

Wei Zhang

arxiv:1712.08844 v1 · 2017-12-23 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D5YWL5D7AZBC7NOARRVR4GEB3P}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:27:16.657637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f7165f47f06422fb5c08c6b1e1881dbe6fa624a30b4155fa412c9f875b56e2a

Aliases

arxiv: 1712.08844 · arxiv_version: 1712.08844v1 · doi: 10.48550/arxiv.1712.08844 · pith_short_12: D5YWL5D7AZBC · pith_short_16: D5YWL5D7AZBC7NOA · pith_short_8: D5YWL5D7

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/D5YWL5D7AZBC7NOARRVR4GEB3P \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 1f7165f47f06422fb5c08c6b1e1881dbe6fa624a30b4155fa412c9f875b56e2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f04ffb1d7f8e653959085d1f7ecd751840812f0c0179d8556df6ef75dfd42e96",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-12-23T21:41:23Z",
    "title_canon_sha256": "a26c329d435245f9835250964407ffc5311a94513c2b7c25ec5edd4d42f3d215"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.08844",
    "kind": "arxiv",
    "version": 1
  }
}